Question

In 1897 the Swedish explorer Andreé tried to reach the North Pole in a balloon. The balloon was filled with hydrogen gas. The hydrogen gas was prepared from iron splints and diluted sulfuric acid. The reaction is

Fe(s)+ H2SO_4(aq) -----> FeSO4(aq) + H2(g)
The volume of the balloon was 4800 m^3, and the loss of hydrogen gas during filling was estimated at 20.%. What mass of iron splints and 98% (by mass) H2SO4 were needed to ensure the complete filling of the balloon? Assume a temperature of 0^C, a pressure of 1.0 atm during filling, and 100% yield

Answer 1

`m_(Fe)=59.79x10^6gFe\\m_(H_2SO_4)=107.1511x10^6gH_2SO_4`

Step-by-step explanation:

Hello,

Based on the given data, the corresponding moles of hydrogen to fill the balloon without loss is:

`n_(H_2)=(PV)/(RT)=(1.0atm*4.8x10^6L)/(0.082(atm*L)/(mol*K)*273.15K) =214302.2molH_2`

Now, considering the 20% loss of hydrogen, the amount that ensured the complete filling was:

`n_(H_2)=(214302.2molH_2)/(0.2)=1071511molH_2`

Based on that result, we proceed to computed the amounts of both iron and 98% by mass sulfuric acid that were needed to ensure the complete filling of the balloon as follows:

`m_(Fe)=1071511molH_2*(1molFe)/(1molH_2) *(55.8gFe)/(1molFe) =59.79x10^6gFe\\m_(H_2SO_4)=1071511molH_2*(1molH_2SO_4)/(1molH_2) *(98gH_2SO_4)/(1molH_2SO_4)*(100gH_2SO_4)/(98gH_2SO_4) =107.1511x10^6gH_2SO_4\\`

Best regards.